The short answer: yes, this can happen and when it does it is normal, although it tends to be a less common experience. The vast majority of time you clear beliefs or emotions, you will not have experiences like this.
When you have more intense symptoms like this, it often means you are releasing something very deep that affected you intensely, whether or not you are consciously aware of it.
Take this story for an example:
This happened to me (Justin) once when I discovered and let go one of my biggest, deepest limiting beliefs that ran my life for 20 years. The belief was: I am all alone. I got nauseous within a few minutes of clearing it and was detoxing for a few days afterwards. It was a tectonic release, and my body let go of all kinds of energy / patterns / toxins associated with the belief.
After it let up, I felt incredible and like I was reborn… a new person completely. It was a huge release and liberation, and my life changed radically from that day going forward in the best way.
It sounds like you found something big for you. In these cases it is best to drink lots of water, rest, and integrate as much as possible. Take a break from the clearings for a day or two. If the sick feeling is very mild, you can continue you with the belief and emotional clearing at a more normal pace.
And finally, it is also possible that feeling sick is just a meaningful coincidence as sometimes we get sick for other, normal reasons; and if we happened to do the belief or emotional clearing around the same time we notice it or we get sick shortly thereafter, the mind can incorrectly associate the two experiences when searching for a reason why.